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Writer's pictureKalle Lintinen

Cones of Reflection

In the post I also presented a video of the rotating model of dots with curves (and circles) depicting their path. However, in the post I already noted that the 2D projections are better, so I won’t show the old video here.

 

The video wasn’t exactly wrong, but it was at the same time simplified and not simple enough. This means that depicting reflections using curves is either really hard, or possibly even impossible.

 

So, in this post I decided to show how the reflection of dots works with cones (of reflection). The idea of using cones isn’t new at all to me. I’ve used them in my posts for a while and the (now rejected) Theory of Everything -manuscript used them.

 

However, I didn’t fully understand what the cones were in the old manuscript. I new they were important for refraction, but I honestly didn’t exactly know how a straight flight path could be converted into something that could be illustrated with a cone (or more precisely two cones).

 

I did have an idea that the presence of dots around dots would prevent them moving in a straight line. I didn’t really have a proper idea how this prevention worked. Now that I finally understand that the only interaction is reflection, I also understand that the cones are cones of reflection. However, in the case of entangled helices of dots, something really curious happens to the cones of reflection. While the actual two cones cone must be drawn on either side of the plane of refraction, their effect must be shifted by the radius of the dot. This is because the dots have a size and the reflective interaction is transferred to another location defined by the sum of two vectors: both of the vectors passing from the center to the surface.

 

Using three dots, the reflective interactions look like this: 

Already this image/video looks a bit complicated but should be more accurate than the complex image/video of my last post.

 

My next task is to add a fourth dot (with its cones) to the image and still keep it clear. If I’m very brave, I might also include vectors of movements. But only if these vectors clarify the image.  

 

 

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